I agree that corn shouldn't supplant a large portion of the feed since it is low in protein and other nutrients. Corn should only be fed in small amounts and not in place of a specially formulated feed which have all the necessary nutrients needed for healthy birds and good quality eggs.
However, chickens need the high energy content to keep warm in the worst of the winter weather, since their body reserves are quickly used up, particularly on cold winter nights. Increasing the birds calorie intake and thus provide them with more energy to keep themselves warm. Winter temps will increase feed consumption because of the hens’ increased need for energy to maintain body temperature. This is also due to the shorter days so the birds spend much less of their day eating and are idle on a cold roost.
Corn, milo, barley and wheat all have high carbohydrates to fiber ratios so do aide in providing the energy needed in cold weather.
Studies
From Utah State University "A chicken will stop eating once a certain quantity of energy has been consumed in a day. This will happen even if the bird has not ingested enough protein or vitamins. Therefore, the energy concentration needs to be in balance with the other nutrients in the diet."
http://extension.usu.edu/files/publications/publication/ag_poultry_2008-02pr.pdf
Church et al. (1989) determined the combustible energy, gross energy, utilization efficiency, assimilated energy, and metabolizable energy from seeds ...(based on studies of the consumption of Prairie Chickens in Minnesota during December, January and February)... rank them as follows.
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Excellent -- millet, soybeans
Good -- sunflowers, lespedeza
Fair -- wheat, corn, sorghum (the soybeans were probably selected for the protein in the absence of insects)
http://www.npwrc.usgs.gov/resource//birds/sheyenne/winter.htm
http://www.wvu.edu/~agexten/poultry/pfs17.pdf
http://www.ag.ndsu.edu/pubs/ansci/beef/as1238.pdf
http://www.agriculture.com/livestock/poultry/feed/feeding-freerge-chickens-in-winter_292-ar28128